The great flurry of activity which followed the announcement of Ziegler and Natta's initial results has led to the discovery of an enormous number of catalyst systems which are effective in stereospecific polymerization. However, there is little more understanding now than in 1955 of how most of these systems work. Now that the initial excitement has cooled, a larger amount of thoughtful work on the mechanisms of these reactions should appear. As a basis for understanding both the heterogeneous and homogeneous systems, more mechanism studies in organometallic chemistry are urgently needed. More specifically for the heterogeneous catalysts, continued attempts should be made to find better models for the active sites, and new analytical methods should be sought to provide more information concerning the active site itself. In homogeneous systems, greater understanding of the ion pairs, the structure of which is so critical, could be obtained by the preparation and study of nonpolymeric analogues. In addition to understanding better the catalysts that we already have, we may see in the future the development of new kinds of catalysts. Some of these may be capable of producing polymers in which the units have a more complex code than in those produced by simple stereospecific catalysts. Such catalysts already exist in nature. For example, we now know that the RNA molecule functions as a multifunctional catalyst in peptide syntheses, each sequence of three bases along the backbone corresponding to a particular amino acid. The molecule consequently acts as a catalytic template which defines the order in which these amino acids polymerize into the final peptide (32). Synthetic RNA's have also been prepared containing only one base such as uracil along the chain (33). Since three uracil units correspond to phenylalanine, the polyuracil acts as a template for the formation of a peptide containing only this amino acid. There seems no reason why, ultimately, we should not be able to synthesize polymeric catalysts of this type which can act as templates for the polymerization of specific monomers other than those found in living systems. If a number of systems such as this can be found, we will be on the road to producing catalysts which can not only control the stereochemistry of a polymer chain but also the order in which a group of different monomers can enter into it.